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## Answers

**Given : secx + tanx = p ................................... (i)**

**Now, we know that : sec²x - tan²x = 1**

**or, (secx + tanx)(secx - tanx) = 1**

**Putting (i) in the equation, we get :-**

**p(secx - tanx) = 1**

**or, secx - tanx = 1/p .........................................(ii)**

**Now adding (i) and (ii), we get :-**

**secx + tanx + secx - tanx = 1/p + p**

**or, 2secx = (1+p²)/p**

**or, secx = (1+p²)/2p [**

**Ans 1****]**

**On subtracting (ii) from (i), we get :-**

**(secx + tanx) - (secx - tanx) = p - 1/p**

**or, 2tanx = (p² - 1)/p**

**or, tanx = (p² - 1)/2p [**

**Ans 2****]**

**We know that sinx = sinx/cosx x cosx**

**or, sinx = tanx x 1/secx**

**or, sinx = tanx/secx**

**or, sinx = [(p² - 1)/2p]/[(p² + 1)/2p] ..(In the next step both the 2p get cancelled)**

**or, sinx = (p² - 1)/(p² + 1) [**

**Ans 3****]**

**Hope that helps !!**